Optical brightening agents (OBAs) are additives used to enhance the appearance of color of fabric and paper. In particular, OBAs cause a “whitening” effect that makes materials look less yellow by increasing the overall amount of blue light reflected.
Sometimes, “whiteness” represented as a single number is not sufficient for the study of OBA-enhanced paper or fabric samples. Instead, a total spectral radiance factor (TSRF) is used to express more detailed information about a sample. TSRF is defined as the ratio of spectral radiance illuminated and observed under the same conditions at wavelength λ of an observed fluorescent sample and of a completely diffuse, non-fluorescent, perfectly reflecting surface. Alternatively, TSRF may be defined as the ratio of the flux intensity at wavelength λ returned from the fluorescent sample and from the completely diffuse reflecting surface in the same solid angle of the same direction, when illuminated under the same conditions. Thus, TSRF may be expressed as:B(λ)=S(λ)/S0(λ)  (EQN. 1)where S(λ) is the intensity at wavelength λ of the radiant light returned by the fluorescent sample, and S0(λ) is the intensity at wavelength λ of the radiant light reflected by the completely diffuse reflecting surface.
In general, B(λ) includes two parts, as expressed below:B(λ)=R(λ)+φ(λ)  (EQN. 2)where R(λ) is the reflection spectral radiance factor (i.e., reflectance) and φ(λ) is the fluorescent spectral radiance factor.
Although R(λ) is purely sample related, φ(λ) is the ratio of fluorescent light and diffuse reflection of the illuminant light and depends on the light source as well as on the sample. For different instruments, the spectral power distribution of the light source can be dramatically different; thus, the directly measured TSRF of the same sample by different instruments can vary dramatically. Conventional approaches that compensate for instrument differences are algorithmically complicated and require prior knowledge of certain measurements.